Runlength-limited (RLL) codes have been widely used in magnetic and optical data storage to eliminate sequences that are undesired for the processes of recording and reproducing digital data. Various classes of RLL codes are used in practice. For example, peak detection systems employing runlength-limited RLL(d,k) constrained codes such as rate-1/2 RLL(2,7) and rate-2/3 RLL(1,7) codes have been predominant in digital magnetic storage at low normalized linear densities. At moderate normalized linear densities, the introduction of partial-response maximum-likelihood (PRML) detection channels into data storage required a different type of constrained codes. This class of codes, which are known as PRML)G,I) codes, facilitates timing recovery and gain control and limits the path memory length of the sequence detector, and therefore the decoding delay, without significantly degrading detector performance.
Noise-predictive maximum likelihood (NPML) channels in magnetic recording, which generalize the PRML concept, have detector targets with spectral nulls at DC and/or the Nyquist frequency 1/(2T). Therefore PRML(G,I) codes in conjunction with 1/(1⊕D2) precoders can also be used in NPML channels. PRML(G,I) codes may also satisfy a VFO constraint, which is also known as the M constraint at the input of a 1/(1⊕D2) precoder. The VFO constraint allows discrimination of encoded data from the synchronization preamble and fast start-up of the PRML receiver. This class of RLL codes satisfying G, I and M constraints are known as PRML(G,I,M) codes. The recorded VFO pattern . . . ++−−++−− . . . is received as a tone with frequency 1/(4T) at the center of the channel. The concept of excluding data patterns with spectral component at 1/(4T), namely the VFO constraint or M constraint at the input of a 1/(1⊕D2) precoder, was generalized by the introduction of anti-whistle codes that exclude data patterns with zero or one spectral component in the frequency band (0, 1/(2T)).
Error-correction coding (ECC) algorithms are often described using finite-field arithmetic. Finite fields have n elements where n is a power of a prime number. Finite fields were invented by Galois and therefore are also known as Galois fields (GF). As used herein, “GF(n)” denotes a Galois field with n elements. The RLL code parameter that is most critical to determining error-rate performance in the presence of ECC is error propagation. Two-way interleaved Reed-Solomon (RS) encoding over GF(16) (where ECC symbol size is s=4 bits or one nibble) have been proposed to increase robustness of headers in a codeword quad (LTO 4) or in a synchronized codeword object (LTO 5) without increasing header redundancy. As almost all of the random error patterns at the detector output are 2 to 5 NRZI bits long (short error bursts of non-fading type), error propagation is defined herein as the maximum number of erroneous symbols in a RS codeword that is caused by a channel error burst not longer than 5 NRZI bits. In general, the header RLL scheme and the header RS-encoding scheme should be selected such that a likely error event in the channel can only give rise to at most one erroneous symbol per RS codeword. There remains a need for a RLL design which minimizes error propagation.